Order of Operations (PEMDAS) — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
5 + 6 × 3 = 33
Corrected: 5 + 6 × 3 = 23
The corrected sentence is: "5 + 6 × 3 = 23" The error was left-to-right error — added before multiplying: the original sentence "5 + 6 × 3 = 33" needed to be fixed.
2. Fix the sentence:
16 - 6 ÷ 2 = 5
Corrected: 16 - 6 ÷ 2 = 13
The corrected sentence is: "16 - 6 ÷ 2 = 13" The error was left-to-right error — subtracted before dividing: the original sentence "16 - 6 ÷ 2 = 5" needed to be fixed.
3. Fix the sentence:
9 × 2 + 4 × 3 = 78
Corrected: 9 × 2 + 4 × 3 = 30
The corrected sentence is: "9 × 2 + 4 × 3 = 30" The error was grouped incorrectly — computed 9 × 6 × 3 instead of (9×2)+(4×3): the original sentence "9 × 2 + 4 × 3 = 78" needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In PEMDAS, the M stands for Multiplication.
M stands for Multiplication because PEMDAS lists the operations in order: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
2. 8 + 5 × 4 = 28.
Multiply first: 5 × 4 = 20, then add 8 to get 28. PEMDAS says multiplication comes before addition.
3. 30 ÷ 5 + 7 = 13.
Divide first: 30 ÷ 5 = 6, then add 7 to get 13. Division is handled before addition in the order of operations.
4. 2 × 9 - 3 × 4 = 6.
Do both multiplications first: 2 × 9 = 18 and 3 × 4 = 12, then subtract to get 18 - 12 = 6.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why does 12 - 4 × 2 equal 4 and not 16?
Sample answer: You must multiply before subtracting. 4 × 2 = 8, then 12 - 8 = 4. Subtracting first gives the wrong answer of 16.
A good answer includes: You must multiply before subtracting. 4 × 2 = 8, then 12 - 8 = 4. Subtracting first gives the wrong answer of 16.
2. In PEMDAS, multiplication and division are done left to right. Show how to solve 24 ÷ 4 × 3.
Sample answer: Work left to right: 24 ÷ 4 = 6, then 6 × 3 = 18. You do not multiply first because division comes first reading left to right.
A good answer includes: Work left to right: 24 ÷ 4 = 6, then 6 × 3 = 18. You do not multiply first because division comes first reading left to right.